During the Late Triassic, the Newark rift basin of Eastern North America was in the interior of tropical (2.5-9.5 degrees N) Pangaea. Strikingly cyclical lacustrine rocks comprise most of the 6770 m of continuous core recovered from this basin by the Newark Basin Goring Project. Six of the seven drill cores (each from 800 to 1300 m long) from this project are used to construct a composite lake-level curve that provides a much needed record of long term variations in continental tropical climate. The correlations on which the composite section is based show complete agreement between lake level cycles and independent magnetic polarity boundary isochrons. The main proxy of lake level and hence climate used to construct this lake level curve is a classification of water-depth related sedimentary structures and fabrics called depth ranks. We then use Fourier frequency analysis (both FFT and multitaper methods) and joint time-frequency approaches to resolve the periodic properties of the cyclicity and the secular drift in those properties. A consistent hierarchy in frequencies of the lake level cycles is present throughout the Late Triassic (and earliest Jurassic) portions of the cores, an interval of about 22 m.y.. Calibration of the sediment accumulation rate by a variety of methods shows that these thickness periodicities are consistent with an origin in changes in precipitation governed by celestial mechanics. The full range of precession-related periods of lake level change are present, including the two peaks of the similar to 20,000 year cycle of climatic precession, the two peaks of the similar to 100,000 year eccentricity cycle, the single peak of the 412,900 year eccentricity cycle, and the similar to 2,000,000 year eccentricity cycle. There is also good correspondence in the details of the joint-time frequency properties of lake level cycles and astronomical predictions as well. Even in an ice-free world, the tropical climate of Pangaea responded strongly to astronomical forcing, suggesting that precession-dominated climatic forcing probably always has been a prominent feature of tropical climate.